## Coincidence theorem and saddle point theorem

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- by H. Komiya
- Proc. Amer. Math. Soc.
**96**(1986), 599-602 - DOI: https://doi.org/10.1090/S0002-9939-1986-0826487-0
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## Abstract:

We discuss Browder’s coincidence theorem and derive a saddle point theorem from it.## References

- Felix E. Browder,
*The fixed point theory of multi-valued mappings in topological vector spaces*, Math. Ann.**177**(1968), 283–301. MR**229101**, DOI 10.1007/BF01350721 - Felix E. Browder,
*Coincidence theorems, minimax theorems, and variational inequalities*, Conference in modern analysis and probability (New Haven, Conn., 1982) Contemp. Math., vol. 26, Amer. Math. Soc., Providence, RI, 1984, pp. 67–80. MR**737389**, DOI 10.1090/conm/026/737389 - Nelson Dunford and Jacob T. Schwartz,
*Linear operators. Part I*, Wiley Classics Library, John Wiley & Sons, Inc., New York, 1988. General theory; With the assistance of William G. Bade and Robert G. Bartle; Reprint of the 1958 original; A Wiley-Interscience Publication. MR**1009162** - Ky. Fan,
*Fixed-point and minimax theorems in locally convex topological linear spaces*, Proc. Nat. Acad. Sci. U.S.A.**38**(1952), 121–126. MR**47317**, DOI 10.1073/pnas.38.2.121
—, - Ky Fan,
*Extensions of two fixed point theorems of F. E. Browder*, Math. Z.**112**(1969), 234–240. MR**251603**, DOI 10.1007/BF01110225 - Chung Wei Ha,
*Minimax and fixed point theorems*, Math. Ann.**248**(1980), no. 1, 73–77. MR**569411**, DOI 10.1007/BF01349255 - Shizuo Kakutani,
*A generalization of Brouwer’s fixed point theorem*, Duke Math. J.**8**(1941), 457–459. MR**4776** - John L. Kelley and Isaac Namioka,
*Linear topological spaces*, Graduate Texts in Mathematics, No. 36, Springer-Verlag, New York-Heidelberg, 1976. With the collaboration of W. F. Donoghue, Jr., Kenneth R. Lucas, B. J. Pettis, Ebbe Thue Poulsen, G. Baley Price, Wendy Robertson, W. R. Scott, and Kennan T. Smith; Second corrected printing. MR**0394084** - S. Simons,
*Two-function minimax theorems and variational inequalities for functions on compact and noncompact sets, with some comments on fixed-point theorems*, Nonlinear functional analysis and its applications, Part 2 (Berkeley, Calif., 1983) Proc. Sympos. Pure Math., vol. 45, Amer. Math. Soc., Providence, RI, 1986, pp. 377–392. MR**843623**, DOI 10.1090/pspum/045.2/843623 - Wataru Takahashi,
*Nonlinear variational inequalities and fixed point theorems*, J. Math. Soc. Japan**28**(1976), no. 1, 168–181. MR**399979**, DOI 10.2969/jmsj/02810168 - Wataru Takahashi,
*Recent results in fixed point theory*, Southeast Asian Bull. Math.**4**(1980), no. 2, 59–85. MR**655748**

*A generalization of Tychonoff’s fixed point theorem*, Math. Ann.

**142**(1961), 305-310.

## Bibliographic Information

- © Copyright 1986 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**96**(1986), 599-602 - MSC: Primary 47H10; Secondary 49A40, 54H25
- DOI: https://doi.org/10.1090/S0002-9939-1986-0826487-0
- MathSciNet review: 826487